a model for cutting ability

Cliff Stamp

BANNED
Joined
Oct 5, 1998
Messages
17,562
Recently I proposed how to model edge retention and showed a few examples of it in use :

http://www.bladeforums.com/forums/showthread.php?t=416896

http://www.bladeforums.com/forums/showthread.php?t=420917

Now for a harder question, can you model cutting ability? Under a specific amount of force can you predict how deep a blade cuts and how this changes with repeated cuts? Can you model this :

chart2.gif


These are CATRA tests done by Buck knives to promote the Edge 2000 sharpening method. Buck reduced the angles from 35-50 degrees included to 26-32 degrees included and switched to a harder sharpening medium and thus removed the convexing of the cloth wheels. This work (2001) showed blades which cut better initially but cut better for longer. The effect of geometry was so significant that a 420HC blade with the flatter and more acute edge outcut both a ATS-34 and BG-42 blade with the older thicker convex edges. Now if you also re-profiled the BG-42/ATS-34 blades they would of course outperform the 420HC blade as shown here :

chart1.gif


Now this had been known for years to those active on rec.knives and I had discussed it in detail in many reviews showing how changing the angle and as well the grit had the same effect. This was based on work by Swaim and Talmadge. Swaim had been doing it for years when I entered the discussions (lurking) in 1998. Now as to the model - cutting ability is basically inversely proportional to the force on the blade. Now ignoring friction (which is usually valid for several reasons) the force on a blade due to wedging is just a constant determined by the cross section which doesn't change during the cutting plus the force against the very edge which is essentially the bluntness which I have modeled before. Thus the cutting ability is then :

Code:
CA(x)=CA_0/(1+b*x^c)

Where CA(x) is the cutting ability after a given amount of cuts in the test medium (x). CA_0 is the initial cutting ability with no blunting, which is a function of the stiffness of the media and the shape of the blade and initial sharpness. The constants b and c relate how and at what rate the blade blunts. These are the same coefficients as noted in the above linked posts as that part of the equation is of course the equation which I previously used to model sharpness. Ok, now does it work :

buck_catra_bg_420HC.png


Those points are data digitized from the CATRA graphs which is why the axis are scaled (yes I could scale it back, there just isn't any point). The model replicates both early and late stage cutting ability. As noted eariler, Swaim predicted this behavior back in 1998 where he first noted his opposition of greater angles=better edge retention, one of many myths which still persist. I'll be using this model shortly to discuss the hemp cutting and other work I have done. I wanted to use a CATRA model first as it is completely independent data. I will also be using examples of other similar tools, like dental scrapers and such just to show the more general implications. Note I didn't quote the numbers that come out of the model in the above because I didn't have the raw data. I will have all of this for the data I have collected so I'll discuss some of the issues in more detail when I use that.

As a side note, the CATRA curves also show the self-sharpening effect which I first noted in late 1999 during work with Boye blades. The sharpness can decrease then rebound as the edge chips, wears smooth, and this pattern repeats. I had been meaning to look at these curves in more detail for awhile but got distracted with other work. Note in the above I modeled the force in a simple manner :

F_w+F_e

Or force due to wedging (F_w) plus force on the edge (F_e), you can actually break this up and model the force due to wedging in components and thus separate the effect of edge angle and thickness. You can also use this model to do something like compare the edge retention of two blades at different geometries because it is a multi-variable model which includes both geometrical and steel properties. Thus for example you could model the effect of different steels and geometries and thus predict how they would act at different angles or finishes. With a decent spread of steels over different properties (hardness, wear resistance, carbide size) you could also predict the exact properties needed in a steel to give the desired cutting abilities.

Once you have these two coefficients you can also calculate the ratio F_e/F_w which then tells you the fractional dependence of the edge retention on the cutting lifetime. This for example is very high for hemp but very low for soft woods. This shows that you can cut soft wood very well with a blunt blade because most of the force is due to wedging, but trying to cut hemp rope with a dull blade isn't productive. This is why for example makers trying hype blades will do something like cut up a coffee can and then slice wood showing the "superior" edge retention of the knife. In fact because the F_e/F_w ratio is so low for that media the test is nothing but hype. So as a side note, this also lets you quantify hype.

-Cliff
 
Interesting stuff, thanks. As an aside, I got a BG-42 upgrade from Buck and it came sharpened at 20 degrees per side. I was surprised that they didn't grind it the same as the 2K edge. It's been reprofiled, so it's all better now.:D

Gordon
 
I an understand why Buck took the approach they did, using "Edge 2000" is a strong selling point to the masses. However this doesn't explain the origion of the performance and tends to cause confusion where people make incorrect assumptions about cause/effect. If would have been more informative if they just said "We lowered the edge angles and reduced the curvature so they allow them to cut better for longer." It would have also been really nice to give credit to the people like Swaim and Talmadge who had been advocating this for years on rec.knives, knifeforums and bladeforums. This of course would allow people to realize that all they have to do is reduce the edge angles, it isn't unique to Buck. This is how Swaim, Talmage and Johnston discussed the issues on rec.knives, of course they were not selling anything.

Note how many people still try to sell the misinformation of convex edges being superior or that reducing edge angles decreasing the cutting lifetime in spite of the wealth of information such as the above which shows it to be false and dramatically false. So much so that a thin and flat edge on 420HC knife out cuts a heavy convex BG-42 edge. A steel which many describe as "worthless" out cuts a "premium" high speed stainless because it has a more optimal grind - how many people realize this performance relationship? To Buck's credit, they describe the process in detail on a webpage and they did release public and specific information as to why they switched steels and didn't just make some vague comments like "Our tests showed it to be superior.". Fallkniven, Busse and Spyderco also will release the test data they use to make their decisions.

Note as a further aside the 440C blade is clearly inferior to the 420HC blade even after it is reprofiled. This was explored in detail by Landes and Verhoeven who strongly critize 440C as a knife steel because of the edge instability due to the large and segregated carbides. Johnston made the same point on rec.knives long ago, speciifcally comparing 1095 at 65/66 HRC vs Bos ATS-34 in very thin/acute edges.

-Cliff
 
Cliff Stamp said:
Now this had been known for years to those active on rec.knives and I had discussed it in detail in many reviews showing how changing the angle and as well the grit had the same effect. This was based on work by Swaim and Talmadge. Swaim had been doing it for years when I entered the discussions (lurking) in 1998.

And I had known this since the fourth grade, many years before AlGore even invented the internet.

However, the ability to predict and model all this stuff in such detail has me enthralled. I think I would still rather spend my time making and using knives, but the idea of predicting what geometry, angle, grit, and steel would be best for an unfamiliar application sounds super neat. Looking forward to more.
 
the possum said:
And I had known this since the fourth grade ...

Yes, I watched a program on discovery awhile back in which it showed how the basic axe progressed as the metals got harder and stronger and allowed a refinement of the taper from the crude heavy convex bevels of the softer metals to the very strong steel alloys and the very flat and thin bevels. So the basic idea to minimize cross section is a very old one.

Unfortunately on the forums the discussions were often lead by the people selling the knives and thus steel was the focus and the idea that knives cut due to steels was a major point and you often saw argued things like forging improving cutting ability. Some of this still exists now where you will hear forged blades have "better balance" and similar.

Swaim was one of the first guys to stand up and say that was all wrong. Look at the shape of the knife to see how it will perform. How is it ground, what is the weight, where is it balanced. He also discussed both the center of mass and the impact node, noting for example a Cold Steel khukuri was inferior to a Ontario machete because the khukuri had too shallow an impact zone which had too much vibration, especially towards the tip.

Lee's book on sharpening discusses many similar issues, noting the use of very thin bevels, coarser grits for slicing and it predates the discussions on rec.knives by several years. I doubt Lee would claim he invented much of the practices either.

I think I would still rather spend my time making and using knives ...

At the end of the day had I to pick between spending some time in the woods or cutting up piles of stock materials it isn't much of a decision. However it gives me something to do when it rains and you can't do much felling in the dark anyway.

-Cliff
 
I’ve considered starting a thread about these so called super steels. I’ve got a S30V Native, a D2 Grip, and a Kershaw Leek with 440A. To be honest I not sure I can detect a difference in them as far as cutting. Granted I don’t do anything aggressive with them, the hardest use being cutting up cardboard boxes around the house. Now I realize that these aren’t the steels shown in the graph but I’d be surprised if the results were dramatically different.

What I see is 420HC blade steel holding there own against other more highly (at least on these forums) rated blade steels. So am I correct or am I interpreting the graphs wrong.
 
gbaker said:
What I see is 420HC blade steel holding there own against other more highly (at least on these forums) rated blade steels. So am I correct or am I interpreting the graphs wrong.

No you are correct, that would indeed be one way to interpret the graphs. Consider that at the end of the second graph, which shows both blades reground, the difference between the BG-42 and 420HC blade is only about a cut depth of 2, which is about 5% of the optimal ability. Thus unless you can actually measure this difference by hand, which is unlikely, the blades will be identical in hand.

A lot of it also depends on how easily you can sharpen the steel to high levels. If for example you easily restore the Leek to a blazing level of sharpness but you have to do more work with the S30V/D2 blades and don't always get them as sharp, then this could indeed give the Leek an actual advantage. This is why many people have critized some of the more coarse steels like 440C because they had problems getting them very sharp initially. By this I don't mean cut paper, I mean shave above the skin and similar.

-Cliff
 
Quote:

Originally Posted by Cliff Stamp
Now this had been known for years to those active on rec.knives and I had discussed it in detail in many reviews showing how changing the angle and as well
the grit had the same effect. This was based on work by Swaim and Talmadge. Swaim had been doing it for years when I entered the discussions (lurking)
in 1998.

I believe this idea was also widely popularized by John Juranitch before there was an internet. Exsample, In his book and his articles in magazines like Popular Science. I cann't remember everything from back then in rec.knives but I believe those guys offen refered to him when talking about it.
 
Cliff Stamp said:
No you are correct, that would indeed be one way to interpret the graphs. Consider that at the end of the second graph, which shows both blades reground, the difference between the BG-42 and 420HC blade is only about a cut depth of 2, which is about 5% of the optimal ability. Thus unless you can actually measure this difference by hand, which is unlikely, the blades will be identical in hand.

-Cliff

This is indeed a bummer. Could any of the blade steels available show significantly higher edge retention? Say a 5160, or 52100 or the Busse INFI? Has similar testing been done on them?

By the way is this experiment only testing push type cuts or does it also model slicing? The terminology used leads me to believe push cuts only.

As to your second paragraph: I don’t get my knives as sharp as you mention i.e. cutting hairs above the skin. That is just a goal to achieve in the future.
 
After thinking about this. Can you even really get data points to model this with out using a machine to prevent slight slicing and equal pushing? I’m not sure you can ignore friction on the blade or assume wedging forces are equal without some type of machine. Can a real push cut be made without any slicing motion? How much does even a very small sliceing motion effect the cut? I think the questions this type of test produces are many and could be very interesting.
edit to add..
Is the force on the edge the same if the cut is a push or a slice?
 
db said:
I believe this idea was also widely popularized by John Juranitch before there was an internet.

John Juranitch applied a relief grind but the actual sharpened edge was still very obtuse. Swaim's idea was that a more acute edge would still offer a higher cutting lifetime because even if it suffered more wear/damage (which isn't always the case) it took much more steel to be removed to get to the same edge thickness he also promosed the corrosponding geometrical model. Buck didn't simply add a relief bevel like Juranitch they reduced the entire angle significantly like Swaim.

Juranitch did much to promote the idea of relief bevels and acute grinds on knives, unfortunately he didn't clearify relief bevels are the worst way to achive the described goals which has lead to massive misinformation and outright absurd behavior of people sending blades into custom makers to have the edge reground. If you have power equipment you regrind the primary bevel.

gbaker said:
This is indeed a bummer. Could any of the blade steels available show significantly higher edge retention?

Not in the way CATRA shows the results but that is one of the main problems with their work. What most people would ask about edge retention would be something like "How many cod can I fillet before I have to sharpen the knife?" In order to answer that question from the above CATRA graphs you have to use horizontal intersection asymptotes. That is kind of not overly visually obvious and the answer ends up being often being a nonliner function of the extent of blunting. In short, the graphs are not overly useful because of the way they present the data. However consider the following :

catra_intersection.png


The x-axis on this graph is the reduction in cutting ability of the knives and the y-axis shows how much more material the BG-42 blade can cut over the 420HC blade before both reach that same level of degredation. When the blades are cutting about half of optimal, point (1), the BG-42 blade will have cut about 20% more material - not overly impressive. However, when the blades are used down to about 25% of optimal, point (2), the BG-42 blade will have cut over 60% more material.

So if you like to keep your blades very sharp and they are always cutting very close to optimal, that CATRA data doesn't show much of an advantage to BG-42. Since BG-42 it also more expensive and 420HC is tougher, more ductile, easier to grind and more corrosion resistant - it seems obvious that 420HC is the clear winner. However if you are willing to use your blades to very blunt states then BG-42 will have a large advantage.

This is one of the many reasons why there is often so much contention between people when they talk about edge retention. There are also many other issues such as some steels are easier to sharpen and if you don't get a steel optimally sharp the edge retention will be horrible even if it has ideal characteristics to cut a type of material. Then there are issues like what happens if you keep decreasing the angle, or what happens if you harden both blades to near maximum hardnes?

By the way is this experiment only testing push type cuts or does it also model slicing?

CATRA machines do a heavy slice, meaning there is signficant downwards force.

I don’t get my knives as sharp as you mention i.e. cutting hairs above the skin.

As a general starting point anyone should be able to sharpen a knife to slice newsprint well with no hangs. With a little work to refine burr removal this can be increased to a straight push.

db said:
Can you even really get data points to model this with out using a machine to prevent slight slicing and equal pushing?

The model works on any combination of push/slice, note in the derivation there was no mention of how the cuts were made because it doesn't influence the model. It is actually just a general model of something inversely proportional to force. How you interpret the numerical quantities determined are specific to what you are modeling.

I’m not sure you can ignore friction on the blade ..

In general you would represent the forces on a blade by :

Code:
F_w+F_f+F_e

For wedging, friction and edge forces, respectively. Which of the force(s) dominates depends on the characteristics of the media. You can characterize the dependence by the ratio F_i/Sum F_i (i=w,f,e). Tomatos are very sensitive to F_e, turnips are very sensitive to F_w. Materials strongly dependent on F_f are rare, cheese is an example.

...or assume wedging forces are equal without some type of machine.

If you are speaking of on each cuts, you are concerned about the average effect of very many cuts, not the individual effect of each cut. Note the curves I have posted recently are far more consistent than the CATRA curves in the above. By hand, on random cardboard stock, I gathered data which had a much lower variance than the very expensive CATRA machines on special card stock due to basic statistics by brute force application of root square noize reduction. Those CATRA curves look like one shot runs thus each point represents a measure of sharpness. For the graphs I plot each point is determined at times by over 100 measures of sharpness. This reduces the uncertainty in the data by over a factor of ten. There is of course nothing saying you can't repeat a CATRA run of course and averaging them would produce a smooth curve.

The main benefit of CATRA testing is that since you are always using the same stock you don't need benchmark knives because the work itself is constrained as a benchmark. As Goddard has noted many times, a person evaluating the performance of a knife always needs at least one benchmark knife and ideally it is always the same blade. There are other benefits as well to CATRA type testing, some of them are also negatives, such as the fact that since it is so constrained it is the same for whoever runs the machine which means it ignores any effect of the user which has its issues.

Can a real push cut be made without any slicing motion?

Absolute zero is more of a theoretical quantity. In general you would characterize the cut by a force or distance ratio. A 95% push cut would mean the blade moved only 5% of the push distance on a draw or the draw force was 5% of the vertical load or you cold so some kind of average of the two. A person could easily do a push cut which would be insignificant on a draw, this is how chisels and draw knives are used for example.

How much does even a very small sliceing motion effect the cut?

A very small draw would have a corrosponding very small effect, all effects are linear in the limit of being very small as per fundamental calculus. Of course the exact value for "very small" depends on the nonlinearity of the function. It would be hard to argue slicing was highly nonlinear from physical principles and based on what I have seen it isn't. Most people who use tools know this obviously, they are again not thinking of the math, but that is just a language issue. Lee also notes one of these effects in his book and shows how to calculate it for skew cuts on wood which are essentially wood push cuts with a draw component. You note that you need a large draw to induce a large effect because you are essentially smearing out the push cut over a longer distance, so the effect would be :

Code:
influence of draw = (change in cut distance)/(cut distance)

Is the force on the edge the same if the cut is a push or a slice?

Push cuts are highly compressive, slices are more torsional/tensile and the cutting action is very different as I have noted in detail previous posts, you are basically comparing axe/saw. If you do a push cutting hemp rope test vs a slicing hemp rope test you use different finishes (1 micron vs 100 micron). If you reverse them then the performance is horrible for both. This is often how people demonstrate "superior" performance by putting a more optimal finish on the blade which is being sold as "superior".

-Cliff
 
"
Cliff wrote...
John Juranitch applied a relief grind but the actual sharpened edge was still very obtuse.
That is only half correct. John Juranitch says you should design an edge determined on the use of the knife. His rule is to taper, thin , the edge back just short of the point of damage, and or collapse, in its use. That doesn't seem like a very obtuse edge to me.
 
He was speaking of the primary edge/taper there, not the secondary, this is obvious right in the next paragraph where he notes he "hollows grind that taper", and thus he isn't sharpening the very edge obviously. From his origional article in Popular Science :

"Fold one 90-degree corner of a piece of paper in half. Fold in half again, and you have 22.5 degrees. Hold the blade at this angle or slightly less for your primary-edge face (right). "

He grinds the primary lower and discusses this taper in detail.His focus on cutting ability is on the relief grind and not the actual edge bevel. As noted this is very different from what was proposed by Swaim and illustrated in the above by Buck. Steve Bottorff has the entire article on his site :

http://users.ameritech.net/knives/Juranitch1977Feb.htm

It is also filled with a bunch of highly misleading statements like :

"As for sharpening itself, it doesn't make any difference what kind of blade you have. Sharp is sharp, whether you're cutting whiskers, leather, wood, or meat."

Optimal sharpness is very dependent on both the media and how it is cut. Other issues are with his claims about steeling, lubricants on the stone, stainless/carbon steels, etc. . Of course that was 30 years ago, but as far as I know he is still selling he same guides and advocating the same general principles.

-Cliff
 
A full quote from your link.
"
From the link...
Edge design starts with a decision on how much taper to build in, and is determined by what you plan to do with the edge. The rule is to taper it back just
short of the point at which it will collapse when worked most severely.

I'd think edge design means the intire edge not just the relief. As for your mis quote of his on the angles I'd say it was an exsample of primary and secondary edges not a hard edge angle recomendation, he even calls it a trick. I also have issues with some of what he says but the fact he has made the point that thinner edges cut better for more than 30 years is correct. He also has a book witch goes into more detail. In fact if I remember correctly Swaim refered to JJ offen back in the early 90s when posting at rec.knives on this.
 
So ... this would explain why my old Buck 112 with 440C did not cut as well as a new Buck 110 with 420HC when sharpened to about the same angle.

I pretty much reprofile all of my using knives as thin as I can get them, and I'm beginning to understand what some do better than others. My BG-42 Buck 110 also came with a thicker edge, but I reprofiled it to about the same as the "Edge 2000" angle from the 420HC blade it replaced (essentially as thin as I could get it given the primary grind). It now cuts like a freakin' demon.

Hmmm ... how would one quantify "cuts like a freakin' demon" in a Cliff Stamp-esqe analysis and graph?? :D

But that is what I expected.
 
Cliff, This brings back what I used to do to make a living. I worked with guys who would make a mathamatical model of something and I would then go out and FUBAR something, take data and then we would tune up the model to fit the actual field data. That was a lot of fun and I got paid for it. I just posted some data on testing 4 knife steels on as close to the same knife geometry as I could get. My tests are rough compared to yours but maybe some usefull data here. If you believe the tests then it does show that better (different) steels at optimum hardness and geometry will hold an edge longer on abrasive materials. PHIL
 
rhino said:
So ... this would explain why my old Buck 112 with 440C did not cut as well as a new Buck 110 with 420HC when sharpened to about the same angle.

Verhoeven and Landes both critize 440C for the exact same reasons.

db said:
I'd think edge design means the intire edge not just the relief.

You would be wrong :

"Edge design starts with a decision on how much taper to build in, and is determined by what you plan to do with the edge. The rule is to taper it back just short of the point at which it will collapse when worked most severely.


...

For meat cutting, Juranitch hollow-grinds the taper this way: The blade is 0.02 of an inch thick an eighth of an inch behind the cutting edge, and 0.04 of an inch thick one-quarter inch back. The tapering is called ‘relief,’ and its importance cannot be overstressed. A blade with good relief will sharpen quickly; one with poor relief, slowly. Only a blade with good relief will take a superior edge."

Note clearly he isn't talking about the edge angle itself, which as noted he recommends using the angle guide which is very obtuse. Juranitch focused on the adjustment of the geometry of the blade behind the edge, this is completely different than adjusting the angle of the edge itself because doing so would be expected to have a dramatic effect on the failure mechanics of the edge. This is where Mike's hypothesis on how lower edge angles could still increase the lifetime of the cutting ability. This is completely different from the effect of a relief grind.

In fact if I remember correctly Swaim refered to JJ offen back in the early 90s when posting at rec.knives on this.

Yes and generally not favorably :

"John Juranitch's so called "carbon vs. stainless test" was totally worthless, because he didn't document types of blade steels, and their hardnesses. Nor, as you so well point out, did he control for the different patterns of interim sharpening, (or dulling, as the case may
be)."

and :

"It's an interesting read, though if you read it closely, and have been using and sharpening a variety of knives for a variety of chores for awhile, parts of the book will have you rolling on the floor laughing."

Those are Mike, he has similar critisms about other aspects such as steeling and Alvin tore into Juranitch on many issues, stainless, oil, etc. . . Swaim did credit the book as starting him thinking about sharpening and gives obvious credit to Juranitch as having brought focus to the utility of using a relief bevel. He also generally recommended the book with qualifiers like the above.

Phil Wilson said:
...(different) steels at optimum hardness and geometry will hold an edge longer on abrasive materials.

Yes, it is also nice to see public comparisons of any case, especially with references. I have spent many years doing numerical modeling, statistics is a very powerful weapon, you just have to be really careful where you aim it. One of my favorite statistics quotes :

"If you torture data sufficiently, it will yield any conclusion desired."

There is a massive amount of user ability to choose algonrithms, tests, filters, etc. to really move data around and force it to support a specific conclusion. This is why in general you have to be really specific about how you did what you did so it can be checked if that was a sensible approach or not. A lot of times people throw out the raw data before it is smoothed/filtered which I never liked - but it certaintly prevents any annoying questions about method.

-Cliff
 
"
Cliff quoted...
"Edge design starts with a decision on how much taper to build in, and is determined by what you plan to do with the edge. The rule is to taper it back
just short of the point at which it will collapse when worked most severely.

...

For meat cutting, Juranitch hollow-grinds the taper this way: The blade is 0.02 of an inch thick an eighth of an inch behind the cutting edge, and 0.04
of an inch thick one-quarter inch back. The tapering is called ‘relief,’ and its importance cannot be overstressed. A blade with good relief will sharpen
quickly; one with poor relief, slowly. Only a blade with good relief will take a superior edge."

LOL your quoteing 2 different paragraphs. None of that changes the fact JJ was promoting thin edges and that they cut better and last longer over 30 years ago and before the internet. Nice try though. Btw JJ grinds his relief to a burr then raises the angle a little to remove it. This is all in the section under the title of
"
Edge design and sharpening
 
db said:
.. your quoteing 2 different paragraphs.

Yes, the second paragraph defines the terms used in the first, which is common in exposition, and makes it clear he is speaking of the material above the edge, not the edge itself which you would never hollow grind. This is also obvious from the fact that he notes edge thickening with sharpening, and that the equipment he sells sharpens at obtuse angles, far above relief bevels.

None of that changes the fact JJ was promoting thin edges and that they cut better and last longer over 30 years ago and before the internet.

As I repeat again, that was never the point in contention. The above is not about relief bevels as per Juranitch, it is about adjusting the edge angle itself and noting that with a more acute edge angle there is an increase in both the initial cutting ability and edge lifetime. This is at first proposal odd because you would expect the more acute edge to both wear/fracture/deform much easier and thus the cutting performance should decrease more rapidly.

The basic model for why this was so was proposed by Swaim. If you look at the numerical results in detail it should be obvious that there is a different behavior to the graphs with acute edges vs obtuse ones. What happens is the more acute edges have higher power coefficients but lower scaling factors. The basic model for why this is so was proposed by Swaim. The effect of a relief grind is a very different matter because it effects mainly the wedging forces on the blade.

It is of course very true that the idea that thinning the cross section increases the cutting ability is far more dated than rec.knives as I noted in the above. I have seen references to this with design of bronze/copper blades and I assume it goes back to the first stone tools. What Swaim did was important in several respects because he studied the effects in specific detail and provided that detail to the public in a time and in a place where much of the information was in opposition.

Lee's perspective on multi-beveling is similar to Juranitch but is more comprehensive and more clear as to what is being discussed. He doesn't reference where his ideas on multi-beveling come from, outside of his comments on friction, but I doubt he would claim to have invented the whole of it.

-Cliff
 
Back
Top